Ultrasensitive detection of local acoustic vibrations at room temperature by plasmon-enhanced single-molecule fluorescence

Sensitive detection of local acoustic vibrations at the nanometer scale has promising potential applications involving miniaturized devices in many areas, such as geological exploration, military reconnaissance, and ultrasound imaging. However, sensitive detection of weak acoustic signals with high spatial resolution at room temperature has become a major challenge. Here, we report a nanometer-scale system for acoustic detection with a single molecule as a probe based on minute variations of its distance to the surface of a plasmonic gold nanorod. This system can extract the frequency and amplitude of acoustic vibrations with experimental and theoretical sensitivities of 10 pm Hz−1/2 and 10 fm Hz−1/2, respectively. This approach provides a strategy for the optical detection of acoustic waves based on molecular spectroscopy without electromagnetic interference. Moreover, such a small nano-acoustic detector with 40-nm size can be employed to monitor acoustic vibrations or read out the quantum states of nanomechanical devices.


SINGLE-MOLECULE LEVEL
Good photostability is a basic requirement for molecules as fluorescent probes. Thus, 39 we checked the photostability of CV molecules at the single-molecule level. We took would be changed and we extracted the variation by a lock-in amplifier. In this way, 91 we can obtain the resonant spectra of the tuning fork without and with sample as 92 shown in Supplementary Figures 4b and 4c which shows a central resonant frequency 93 of 32.758 and 32.714 kHz, respectively. The Q factor decreases from 5,000 to 2,000 94 after the sample is attached due to additional dissipation. For the following acoustic 95 detection measurements, we fixed the frequency of the tuning fork to be on resonance 96 to generate the strongest acoustic wave. It is worth noting that the resonant frequency 97 of the tuning fork slightly varies from sample to sample. Thus, we have to 98 characterize the resonant spectrum of each sample before measurements.  which is far less than that of CV molecules without gold nanorod, further confirming that the 132 bright spot of fluorescence is truly enhanced by the nearby gold nanorod. 133

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We also estimated the probability to find a molecule in the near field of a gold 135 nanorod. The estimation can be divided into three steps. First, we calculated the 136 number of CV molecules in the photoexcitation field. The photoexcitation field's 137 volume was calculated to be 1.510 7 cm 3 according to the excitation area of 7.510 5 138 cm 2 and the film thickness of 2.010 3 cm. Then, the number of CV molecules in the 139 photoexcitation field was determined to be 5.010 6 according to the concentration of field's volume of 1.510 7 cm 3 . Unfortunately, the thickness of the fabricated film in 145 our experiment is very inhomogeneous due to the high boiling point of the DMSO 146 solvent, which is hard to evaporate quickly during spin-casting. However, for our 147 experiments, we selected thick areas for investigation in order to scratch the film 148 easily. In that case, the number of gold nanorods in the thick area may be much higher 149 than that in the other thin areas. Therefore, we roughly estimated the number of gold 150 nanorods in the thick area to 10 times higher than the average number. Thus, the 151 number of gold nanorods in the photoexcitation field is 2.010 4 . Last, we calculated 152 the probability to find a molecule near a gold nanorod in the photoexcitation field. We 153 only need to calculate the ratio between the total volume of these gold nanorods and 154 the photoexcitation field volume since the size of a molecule is 2 nm and can be 155 neglected. The volume of a single gold nanorod was calculated to be about 156 810 18 cm 3 according to the size of 3516 nm and the molecule-nanorod distance of 157 5 nm. Therefore, the probability of a single molecule being located near a gold 158 nanorod is 1.010 6 according to the number of 2.010 4 and the photoexcitation 159 field's volume of 1.510 7 cm 3 . Since we have 5.010 6 molecules in the excitation 160 area, we would be able to detect 5 molecules which is reasonably in agreement with 161 our experimental results.   Maxwell's equations to obtain these parameters.

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In this work, both F exc and F em were numerically calculated based on a where E is the local field intensity and E 0 is the incident field intensity. Ohmic loss. Finally, we calculated the radiative decay rate enhancement (F rad ) and 345 the additional nonradiative decay rate (K nr ) using the following Supplementary   346 Equations (4) 4,5 :

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F rad increases sharply when the molecule-tip distance is less than 0.5 nm and decreases 364 exponentially when the distance is greater than 0.5 nm. K nr decays exponentially as a function of 365 distance, but it decreases more sharply than F rad . 366 367 369 We calculated the radiative decay rate enhancement (F rad ) and the additional 370 nonradiative decay rate (K nr ) as functions of the emission wavelength for the 371 point-like dipole of a CV molecule located at a fixed molecule-tip distance of 5 nm.

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As can be seen from Supplementary Figures 11a and 11b, both F rad (red spheres) and Supplementary Equation (7): Finally, we can obtain the whole calculation for the theoretical detection sensitivity of 416 the acoustic wave, which is given by the Supplementary Equation (8): As a result, at room temperature we could achieve the theoretical detection    In principle, the structure of the CV molecule is much rigid due to the strong covalent 566 bonding compared to the distance change based on the weak inter-molecule 567 interaction. It is difficult for the weak acoustic strains to induce a conformational 568 change of a rigid CV molecule. Thus, we think it is a fair assumption to neglect 569 changes of molecular conformation for such small displacements. Moreover, as our 570 detection frequency is much lower than the vibration frequencies of chemical bonds, 571 coupling between them can be safely neglected.